Regularization in Parallel Imaging Reconstruction

INTRODUCTION The recent advance of the parallel MRI technology, which utilizes multiple RF receiver array coils [1], has also demonstrated the capability to enhance the spatiotemporal resolution of MRI [2, 3]. In parallel MRI, there exist two major sources in image reconstruction: the first is the reduced data samples in accelerated scans compared to the unaccelerated scans. The second source of noise is the unfolding of the aliased images, which are derived from the reduced sampling and the Nyquist criterion in Fourier imaging. In this study, we focus on the efforts to reduce the noise amplification from this latter cause. We propose to use full field-ofview prior information to condition the encoding matrix, which accounts for the genesis of the observed aliased images in individual RF receivers. The incorporation of prior information is mathematically formulated using the Tikhonov regularization framework. We resort to different approaches to estimate the regularization parameters, including L-curve [4], and SNR-based direct regularization. The employment of the prior information may decrease the contrast in dynamic scan, while the overall CNR performance has not been investigated. Thus we perform simulations and experiments to study the performance of the regularized parallel image reconstruction in functional MRI experiments. We expect the efforts of optimizing the parallel MRI in brain MRI can be utilize in the investigation of human brain structure and function by improved spatiotemporal resolution and image quality. METHOD In our recent publication [4], we successfully derived the solution of the parallel MRI reconstructions incorporating the prior information using the Tikhonov regularization framework, including the derivation of the associated g-factor metric. We proposed to estimate the regularization parameter using L-curve technique by searching the “elbow” region in the plot of prior error versus model error in the log-log scale [4, 5]. Alternatively, SNR-based direct regularization method is the other approach to estimate the regularization parameter. The SNR of linear equation using whitening observation is then estimated as 1 / ) ~ ~ ( − ≈ c H n y y SNR , where c n is the number of the array channel. Given the SNR estimate, we estimate the regularization parameter from the power spectrum of the singular values of the whitened encoding matrix by searching the singular value with index k such that following cost function is minimized: